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1. Solve the given differential equation, subject to the initial conditions:
. x2y''-3xy'+4y = 0
. y(1) = 5, y'(1) = 3
2. Find two linearly independent power series solutions for each differential equation about the ordinary point x=0
Y'' - xy' - (x+2)y=o
3. Use the definition of the Laplace Transform, to find
L{e-t cosht}
4. Find f(t) if : f(t)=L-1
5. Solve : y'+y= f(t)
where: f(t) = { 1 if 0 ≤ t < 1
{-1 if t ≥ 1
Recall that if f(t) = { g(t) if 0 ≤ t < a
{ h(t) if t ≥ 1
Then f(t)=g(t)-g(t)u(t-a)+h(t)u(t-a)
6. y'(t) = cos t+
Previous year's budget was 12.5 million dollars. This year's budget is 14.1 million dollars. How much did the budget increase? Last year's budget must be subtracted from this y
Example of Decimal to Fraction Conversion: Example: Convert 18.82 to a mixed number. Solution: Step 1: 18.82 is 18 and 82 hundredths. 18.82 = 18(8
In the introduction of this section we briefly talked how a system of differential equations can occur from a population problem wherein we remain track of the population of both t
Combined Mean And Standard Deviation Occasionally we may need to combine 2 or more samples say A and B. Therefore it is essential to identify the new mean and the new standard
Write 3.5 × 104 in decimal notation? Move the decimal point 4 places to the right to get 35,000.
Geometric mean - It is a measure of central tendency normally utilized to measure industrial increases rates. - It is explained as the nth root of the product of 'n' observa
Find out the volume of the solid obtained by rotating the region bounded by y = x 2 - 2x and y = x about the line y = 4 . Solution: Firstly let's get the bounding region & t
how to solve the equation of an inverse function
1. Consider the trigonometric function f(t) = (a) What is the amplitude of f(t)? (b) What is the period of f(t)? (c) What are the maximum and minimum values attained by
if a&b are aconsra
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